Need help with these 4 brainteasers (hard)

[Guest]

hi everyone ive got these brainteasers and they are driving me crazy i seriously need help

ok here they are:

1.)You have a chessboard with white squares and black squares that are each 3" x 3". What is the area of the biggest circle you could draw on the chessboard so that its line only passes through white squares? (It can pass through the corners of black squares, but not anywhere inside)

2.)A group of 8 people were walking their dogs in a park when the dogs all got excited and pulled their leashes from their owner's hands. A stranger quickly ran and caught all the dogs, dragging them to the group of people, and handed each of the owners a leash at random. What are the odds that exactly 7 of the owners received the dog that was his/hers?

3.)How long does it take for the second hand of a clock (non-digital) to go around and cross the minute hand each time? (p.s...i asked this one in another forum and they said the answer was 61 but no explanation was given)

4.)A certain bragging friend stated, “I only have friends that are women. At least one has two large breasts, at least one has two small breasts & at least one has one of each. Two of my friends have a large right female chest appendage, three have large left breasts, four have small left breasts, and five have small right breasts.” What is the fewest number of women friends he can have so that every statement he said is true?

any help would be much appreichiated + please show your logic...

[Guest]

so that its line only passes through white squares?

Do you mean its circumference?

It can pass through the corners of black squares, but not anywhere inside

What does this mean, exactly? Inside of what? If it passes through a corner, it passes inside, unless you are talking about exactly hitting the point of the corner, and then it doesn't pass through the corner, it merely touches it.

What are the odds that exactly 7 of the owners received the dog that was his/hers?

Odds are zero. If 7 of them get their dog, then the 8th must also. Either 6 or 8 of them will have the right dog, it cannot be 7 of them.

How long does it take for the second hand of a clock (non-digital) to go around and cross the minute hand each time?

It's 62 seconds because it takes 60 seconds for the hand to traverse the face of the clock. If you start on 12, then add 60 seconds for the sweep of the second hand, the second hand must then pass :01 becuase that is where the minute hand will be after 1 minute. If the second hand must pass the minute hand, then it will take an additional second.

fewest number of women friends he can have so that every statement he said is true

[LR LL] [LR LL] [sR SL] [sR SL] [sR SL] [sR SL] [sR LL]

[Guest]

I think I get your circle question. The answer would be a circle drawn exactly around a black square. The Pythagorean Theorem says that if the black square has a side of 3” then the diagonal would be about 4.24”. This would also be the diameter of the circle. Area of a circle is Pi times the radius squared. In this case it would be Pi times (2.12" squared), or about 14.12 square inches.

[Guest]

btw, it's appreciated.

If this is for homework, you now cannot turn in your work without plagiarizing me unless you cite my work on this website. So you are either going to fail, be embarrassed, or cheat. I hope it wasn't homework.

[bonanova]

3.)How long does it take for the second hand of a clock (non-digital) to go around and cross the minute hand each time? (p.s...i asked this one in another forum and they said the answer was 61 but no explanation was given)

From noon to 1:00 [3600 seconds] this event happens exactly 59 times [not 60, cuz the minute hand made a revolution, too], at equal intervals.

Crossings therefore occur every 61.01694915254237288135593220339 seconds.

Approximately.

[Guest]

Depends on if you have a "sweeping" second hand or a "interval" second hand. All of my clocks are interval type where the second hand "clicks" one second, every second. This would make the answer 62. If your clock has a sweeping hand, then Bonanova is most assuredly correct.

[bonanova]

Interesting point. The first timepieces [OK, first there were sundials, the ultimate analog timepiece]

had pendulums and escapements, so the hands paused each second. Same deal with pocket and

wrist watches [wheels instead of pendula]. The synchronous motor clock had hands that moved

continuously, like the sundial shadow. Then LED battery burners and LCD battery savers - both

devoid of analog [moving] parts [except a tiny piece of quarts vibrated like crazy] completed the picture.

The question rules out sundials and digitals, but doesn't specify re: discrete/continuous analog.

One might admit 61, 61.017... or 62 as correct. Depends on the paper grader sometimes, too.

p.s. I remember first time I came across the approach I outlined above. A real AHA moment, cuz of early

childhood attempts to mentally solve this. The second hand goes around once. But by then the minute

hand went around by a 60th of a rotation. OK, so move the second hand a 60th of a rotation. But

then the minute hand moved a 3600th of a rotation. Darn. What do you do with an infinite series?

Even when you can do the series, how much nicer to just divide 3600 by 59? It didn't originate with me.

I just remembered so vividly when I first read it, it stayed with me.

[Guest]

Thanks guys these were 4 of 8 brainteasers in a test challenge my friend gave to me a few months back just found it at the bottom of my draw and it annoyed me i got the first 4 and i just had to know the answers for the others. Once again thanks your help has been much appreciated

[Guest]

The second hand goes around once. But by then the minute

hand went around by a 60th of a rotation. OK, so move the second hand a 60th of a rotation. But

then the minute hand moved a 3600th of a rotation. Darn. What do you do with an infinite series?

This leads to a logical fallicy though. I forgot the formal name for it. The concept is that you could never get from point A to point B because of the infinities involved. To get from A to B you must reach 1/2 way. Then you must reach 1/2 way again, then again, and so on for an infinite number of 1/2 way points. Therefore you never reach point B. We all know this is untrue in the "real" world even though it's mathmatically proveable. The fallicy lies in ignoring that at some point, your unit of travel will encompass the entire distance from A to B and you can ingore that 1/2 way point and all future 1/2 way points because you will have arrived at B.

[rookie1ja]

The second hand goes around once. But by then the minute

hand went around by a 60th of a rotation. OK, so move the second hand a 60th of a rotation. But

then the minute hand moved a 3600th of a rotation. Darn. What do you do with an infinite series?

This leads to a logical fallicy though. I forgot the formal name for it. The concept is that you could never get from point A to point B because of the infinities involved. To get from A to B you must reach 1/2 way. Then you must reach 1/2 way again, then again, and so on for an infinite number of 1/2 way points. Therefore you never reach point B. We all know this is untrue in the "real" world even though it's mathmatically proveable. The fallicy lies in ignoring that at some point, your unit of travel will encompass the entire distance from A to B and you can ingore that 1/2 way point and all future 1/2 way points because you will have arrived at B.

Achilles and the tortoise

[Guest]

*Smacks forehead* of course!